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2023 Journal Impact Factor - 0.7
2023 CiteScore - 1.4
ISSN 2083-6473
ISSN 2083-6481 (electronic version)
Editor-in-Chief
Associate Editor
Prof. Tomasz Neumann
Published by
TransNav, Faculty of Navigation
Gdynia Maritime University
3, John Paul II Avenue
81-345 Gdynia, POLAND
e-mail transnav@umg.edu.pl
So, What is Actually the Distance from the Equator to the Pole? - Overview of the Meridian Distance Approximations
1 Gdynia Maritime University, Gdynia, Poland
ABSTRACT: In the paper the author presents overview of the meridian distance approximations. He would like to find the answer for the question what is actually the distance from the equator to the pole - the polar distance. In spite of appearances this is not such a simple question. The problem of determining the polar distance is a great opportunity to demonstrate the multitude of possible solutions in common use. At the beginning of the paper the author discusses some approximations and a few exact expressions (infinite sums) to calculate perimeter and quadrant of an ellipse, he presents convenient measurement units of the distance on the surface of the Earth, existing methods for the solution of the great circle and great elliptic sailing, and in the end he analyses and compares geodetic formulas for the meridian arc length.
KEYWORDS: Great Circle (Orthodrome), Great Elliptic Sailing (GES), Geodetic Aspects, Meridian Distance, Meridian Distance Approximations, Distance from the Equator to the Pole, Polar Distance, Nautical Mile
REFERENCES
Adams, O.S., 1921. Latitude Developments Connected with Geodesy and Cartography. Washington, United States Coast and Geodetic Survey, Special Publication No. 67, p. 132.
AMN, 1987. Admiralty Manual of Navigation, Volume 1, General navigation, Coastal Navigation and Pilotage, Ministry of Defence (Navy), London, The Stationery Office.
Banachowicz, A., 1996. Elementy geometryczne elipsoidy ziemskiej (in Polish). Prace Wydziału Nawigacyjnego Akademii Morskiej w Gdyni, No. 18, p. 17-31, Gdynia.
Bomford, G., 1985. Geodesy. Oxford University Press.
Bowditch, N., 2002. American Practical Navigator, Pub. No. 9, The Bicentennial Edition, National Imagery and Mapping Agency.
Bowring, B.R., 1983. The Geodesic Inverse Problem, Bulletin Geodesique, Vol. 57, p. 109 (Correction, Vol. 58, p. 543).
Bowring, B.R., 1984. The direct and inverse solutions for the great elliptic and line on the reference ellipsoid, Bulletin Geodesique, 58, p. 101-108.
Bowring, B.R., 1985. The geometry of Loxodrome on the Ellipsoid, The Canadian Surveyor, Vol. 39, No. 3.
Dana, P.H., 1994. WGS-84 Ellipsoidal Parameters. National Geospatial Intelligence College, 9/1/94.
Deakin, R.E., 2012. Great Elliptic Arc Distance. Lecture Notes. School of Mathematical & Geospatial Science, RNIT University, Melbourne, Australia, January.
Deakin, R.E., Hunter, M.N., 2010. Geometric Geodesy, Part A. School of Mathematical & Geospatial Science, RNIT University, Melbourne, Australia, January.
Dresner, S., 1971. Units of Measurement. John Wiley & Sons Ltd. May 6.
Earle, M.A., 2000. Vector Solution for Navigation on a Great Ellipse, The Journal of Navigation, Vol. 53, No. 3., p. 473-481.
Earle, M.A., 2011. Accurate Harmonic Series for Inverse and Direct Solutions for Great Ellipse. The Journal of Navigation, Vol. 64, No. 3, July, p. 557-570.
Karney, C.F.F., 2011. Geodesics on an ellipsoid of revolution. SRI International, Princeton, NJ, USA, 7 February, p. 29 - http://arxiv.org/pdf/1102.1215v1.pdf.
Karney, C.F.F., 2013. Algorithms for geodesics. Journal of Geodesy, January, Volume 87, Issue 1, p. 43-55.
Kawase, K., 2011. A General Formula for Calculating Meridian Arc Length and its Application to Coordinate Conversion in the Gauss-Krüger Projection. Bulletin of the Geospatial Information Authority of Japan, No. 59, pp. 1–13.
Michon, G.P., 2012. Perimeter of an Ellipse. Final Answers. www.numericana.com/answer/ellipse.htm
Pallikaris, A., Latsas, G., 2009. New Algorithm for Great Elliptic Sailing (GES), The Journal of Navigation, Vol. 62, p. 493-507.
Pallikaris, A., Tsoulos, L., Paradissis, D., 2009. New meridian arc formulas for sailing calculations in GIS, International Hydrographic Review.
Pearson, F., II, 1990. Map Projection: Theory and Applications. CRC Press, Boca Raton, Ann Arbor, London, Tokyo.
Phythian, J.E., Williams, R., 1985. Cubic spline approximation to an integral function. Bulletin of the Institute of Mathematics and Its Applications, No. 21, p. 130-131.
Snyder, J.P., 1987. Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395.
Torge, W., 2001. Geodesy. Third completely revised and extended edition. Walter de Gruyter, Berlin, New York.
Veis, G., 1992. Advanced Geodesy. Chapter 3. National Technical University of Athens (NTUA), p. 13-15.
Walwyn, P.R., 1999. The Great ellipse solution for distances and headings to steer between waypoints, The Journal of Navigation, Vol. 52, p. 421-424.
Weintrit, A. 2009. The Electronic Chart Display and Information System (ECDIS). An Operational Handbook. A Balkema Book. CRC Press, Taylor & Francis Group, Boca Raton – London - New York - Leiden, p. 1101. - doi:10.1201/9781439847640
Weintrit, A., 2010. Jednostki miar wczoraj i dziś. Przegląd systemów miar i wag na lądzie i na morzu (in Polish) Akademia Morska w Gdyni, Gdynia.
Weintrit, A., Kopacz, P., 2012. On Computational Algorithms Implemented in Marine Navigation Electronic Devices and Systems. Annual of Navigation, No 19/2012, Part 2, Gdynia, p. 171-182.
Williams, E. 2002. Navigation on the spheroidal Earth, http://williams.best.vwh.net/ellipsoid/ellipsoid.html.
Williams, R., 1996. The Great Ellipse on the surface of the spheroid, The Journal of Navigation, Vol. 49, No. 2, p. 229-234.
Citation note:
Weintrit A.: So, What is Actually the Distance from the Equator to the Pole? - Overview of the Meridian Distance Approximations. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 7, No. 2, doi:10.12716/1001.07.02.14, pp. 259-272, 2013
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